http://hdl.handle.net/11716/57 Sun, 26 Jul 2026 16:43:19 GMT 2026-07-26T16:43:19Z http://hdl.handle.net/11716/14248 The role of visualisation in the process of generalisation Zaręba, Lidia In my paper, I discuss the results of individual observations of pupils aged 13-14. These children undertook an attempt to solve problems which were designed in order to bring about an inductive type of generalizing. The main aim of the study was to classify typical methods of proceeding, which represent the pupils’ ways of reasoning and to determine what influence a particular method of proceeding may have on the final outcome of their work. These results indicate the general pupils’ strategies of generalizing. Presumably, visual thinking produces a positive effect on the pupils’ process of generalizing and abilities to describe regularity with the aid of a letter symbol. Thu, 01 Jan 2015 00:00:00 GMT http://hdl.handle.net/11716/14248 2015-01-01T00:00:00Z http://hdl.handle.net/11716/14246 High School Identities Słomczyńska, Katarzyna In 1969, Polish mathematician and logician, Alfred Tarski asked if all the identities true in the set of natural numbers involving the constant 1, addition, multiplication, and exponentiation can be derived from the eleven axioms that are taught at the high school level (High School Identities). In 1981 Alex Wilkie negatively solved this problem by constructing an identity that cannot be proved using these axioms. In this paper we survey results connected with Tarski’s problem. Thu, 01 Jan 2015 00:00:00 GMT http://hdl.handle.net/11716/14246 2015-01-01T00:00:00Z http://hdl.handle.net/11716/14245 O zjawisku zniekształcania obrazu matematyki Olik-Pawlik, Bożena In this paper, we identify the phenomenon of false conviction. We analyze the definition of false conviction and provide the typology of false convictions, including their logical, geometric, cognitive and methodological types. Every type of false conviction is exemplified by empirical data. Thu, 01 Jan 2015 00:00:00 GMT http://hdl.handle.net/11716/14245 2015-01-01T00:00:00Z http://hdl.handle.net/11716/14242 Quasi-arithmetic means Górowski, Jan; Łomnicki, Adam We present a list of geometric problems with solutions that lead to known or less known means. We also prove, by elementary means, some property for so-called quasi-arithmetic means. We use the proved result to justify some inequalities between the means. Thu, 01 Jan 2015 00:00:00 GMT http://hdl.handle.net/11716/14242 2015-01-01T00:00:00Z